Numpy quick start (IV) -- random sampling and general functions

One 、 Random sampling （np.random modular ）

function	effect
np.random.random(size=None)	size yes Integers or Integer tuple ; Generate [0, 1) Random number between
np.random.uniform(a=0.0, b=1.0, size=None)	Generate [a, b) Upper Uniform distribution The random number
np.random.randn(d0, d1, …, dn)	d0, d1, …, dn Control shape ; Generate Standard normal The random number
np.random.randint(a, b=None, size=None)	Generate [a, b) Random on Integers ; When b When omitted , Generate [0, a) Random integers over
np.random.rand(d0, d1, …, dn)	And random.random The effect is the same , It's just size No longer a tuple
np.random.normal(mu=0.0, sigma=1.0, size=none)	Generate Normal distribution The random number

1.1 np.random.random()

print(np.random.random())
# 0.7244562837682348
print(np.random.random(2))
# [0.22283098 0.72975332]
print(np.random.random((2, 2)))
# [[0.30166809 0.39634144]
# [0.75755076 0.9186064 ]]

1.2 np.random.uniform()

print(np.random.uniform(2, 4))
# 2.8381002639487756
print(np.random.uniform(2, 4, (2, 2)))
# [[2.66832969 3.97791269]
# [3.28302481 2.77316893]]

1.3 np.random.randn()

print(np.random.randn())
# 0.07619658670655587
print(np.random.randn(1))
# [0.15591832]
print(np.random.randn(2, 2))
# [[ 1.80289612 1.26520523]
# [-0.18691585 -1.07256013]]

1.4 np.random.randint()

print(np.random.randint(1, 10))
# 2
print(np.random.randint(1, 10, (2, 2)))
# [[2 7]
# [2 3]]

1.5 np.random.rand()

And random.random comparison , More recommended random.rand.

print(np.random.rand())
# 0.4294526669056693
print(np.random.rand(2, 3))
# [[0.98298448 0.93969596 0.1592919 ]
# [0.4399961 0.52320823 0.5306809 ]]

1.6 np.random.normal()

print(np.random.normal(0, 1, (2, 3)))
# [[-1.42867251 1.07133406 -0.41702297]
# [ 0.83092417 0.17981133 2.15503384]]
print(np.random.normal(2, 100, (2, 3)))
# [[ -8.0837793 161.39657097 35.2570548 ]
# [ 72.32855794 51.32771614 10.86325406]]

Two 、 Common mathematics / Statistical function

Common mathematical functions ：

function	effect
np.sin、np.cos	Trigonometric functions
np.sqrt	square root
np.exp	Exponential function
np.log、np.log10、np.log2	Logarithmic function
np.abs	The absolute value
np.sum	Sum up
np.prod	quadrature

Commonly used statistical functions ：

function	effect
np.median	Calculate the median
np.mean	Calculate average
np.std	Calculate the standard deviation
np.var	Calculate variance
np.corrcoef	Calculate the correlation coefficient

3、 ... and 、 Common logic functions

3.1 Truth test

function	effect
np.all(a, axis=None)	Judge array a Along the axis Whether the value in the direction All for True;axis by None Will judge whether the value along all directions is True
np.any(a, axis=None)	Judge array a Along the axis Whether the value in the direction At least one for True

3.1.1 np.all()

A = np.array([[True, False],[True, True]])
print(np.all(A))
print(np.all(A, axis=0))
print(np.all(A, axis=1))
# False
# [ True False]
# [False True]

print(np.all([1, 1]))
print(np.all([1, 0]))
print(np.all([0, 0]))
# True
# False
# False

3.1.2 np.any()

A = np.array([[True, False],[True, False]])
print(np.any(A))
print(np.any(A, axis=0))
print(np.any(A, axis=1))
# True
# [ True False]
# [ True True]

print(np.any([1, 1]))
print(np.any([1, 0]))
print(np.any([0, 0]))
# True
# True
# False

3.2 Comparison function

function	effect
np.array_equal(a1, a2)	If the array a1 and a2 Of The same shape And one of them The elements are the same , Then return to True, Otherwise return to False
np.allclose(a, b, rtol=1e-5, atol=1e-8)	rtol yes relative Tolerance ,atol yes absolute Tolerance ; If the array a and b Within tolerance By element equal , Then return to True, Otherwise return to False

3.2.1 np.array_equal()

print(np.array_equal([1, 2], [1, 2]))
print(np.array_equal(np.array([1, 2]), np.array([1, 2])))
print(np.array_equal([1, 2], [1, 2, 3]))
print(np.array_equal([1, 2], [1, 4]))
# True
# True
# False
# False

3.2.2 np.allclose()

If the array a and b According to the elements, the following inequality is satisfied ：

$$|a-b|\le atol+rtol\cdot |b|$$

be allclose Function will return True. It can be seen that , The above inequality is asymmetric , So we can come to the conclusion that ：

allclose(a, b) and allclose(b, a) In rare cases, they are not equal .

print(np.allclose([1e10, 1e-7], [1.00001e10, 1e-8]))
print(np.allclose([1e10, 1e-8], [1.00001e10, 1e-9]))
print(np.allclose([1e10, 1e-8], [1.0001e10, 1e-9]))
# False
# True
# False